Small form factor, or something like that . Little motherboard possibly fanless, space for one or maybe 2 2.5 hd. The little thing you can use for a nice video player at home or the cash register at work
Great advice in the comments already, I'll just recommend that you familiarise yourself with the rescue boot of a live disc of your distro.
If things go weird with thr move you can boot the live in rescue mode, mount your disks and fix fstab, or even redo the initrd . Don't wait until you need it
Like a giant pressure cooker